9) A rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from
the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?
A) 130 m
B) 150 m
C) 160 m
D) 140 m​

Answer:

-6

Step-by-step explanation:

To find the slope, plug any two of your points into the slope formula.

I'll use your first two; (-2, 8) and (-1, 2).

[tex]\frac{y2-y1}{x2-x1}[/tex]

Your y1 term is 8, your y2 term is 2.

Your x1 term is -2, your x2 term is -1.

[tex]\frac{2-8}{-1-(-2)} \\\\\frac{-6}{-1+2} \\\\\frac{-6}{1} \\\\-6[/tex]

Your slope is -6.

Answer:

The slope is [tex]\huge \boxed{-6}[/tex].

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\displaystyle \frac{2-8}{(-1)-(-2)}=\frac{-6}{1}=-6[/tex]

Therefore, the slope is -6, and the correct answer is -6.

Answer: C

Step-by-step explanation:

plug in y=8 to

x+y=3

x+8=3

x=-5

There is no need to look at the other answer choices since they do not have x equaling to -5.

So,

[tex]x+y=3\Rightarrow y=3-x[/tex]

Then,

[tex]8=3-x\Rightarrow x=-5[/tex]

The ordered pair is therefore,

[tex]C(-5,8)[/tex]

Hope this helps.

r3t40

Answer:

x^2y^2 +9xy^2-xy-27y-6

Step-by-step explanation:

(xy+9y+2) (xy-3)

Each term of second bracket will be multiplied with the terms of first bracket

= xy(xy+9y+2) -3(xy+9y+2)

= x^2y^2+9xy^2+2xy-3xy-27y-6

=x^2y^2+9xy^2-xy-27y-6

Answer:

The correct option is D.

Step-by-step explanation:

Let the number of cars Zane washed on Saturday be x.

It is given that he gets paid $8 for every car he washes and made a total of $64 on Saturday.

We need to write an equation to show how many cars Zane washed on Saturday.

If he get $8 for one car, then the total amount he get for x cars is

Total amount = 8x

He made a total of $64 on Saturday, so

[tex]8x=64[/tex]

The required equation is 8x=64.Therefore the correct option is D.

Answer:

$1.80

Step-by-step explanation:

Based on the ratio shown in the double number line, the cost for 1 pound of avocados is $1.80.

5 pounds = 9$

9 divided by 5 = 1.8$/pound

Answer:

$1.80

Step-by-step explanation:

Note this:

5 lbs of avocado/$9

So, how much for 1 lb?

Remember units!!! They REALLY are important!!

1_lb_ x $9____ = (1 x 9)/5 = 1.8

5 lbs

**where are the numbers in our conversion coming from? Our notes!

We must now convert our answer to $'s, so $1.80 is our answer!

Answer:

x = 6, x = -5, x = 9

if f(x)=(x-6)(x+5)(x-9)

Step-by-step explanation:

The zeros of a polynomial in factored form can be found by setting the polynomial equal to zero and then realizing if a product is zero, then at least one of it's factors is zero.

So we have the zero's are the x's that satisfy

(x-6)(x+5)(x-9)=0.

We just need to solve three equations:

x-6=0

           This can be solved by adding 6 on both sides:  x=6

x+5=0

         This can be solved by subtracting 5 on both sides: x=-5

x-9=0

         This can be solved by adding 9 on both sides: x=9

The solutions are in { 6,-5,9 }.

Answer:

x = 6, x = -5, x = 9

Step-by-step explanation:

If the polynomial f(x) is written in factored form, f(x) = (x − 6)(x + 5)(x − 9), the zeros of the polynomial function are x = 6, x = -5, x = 9.

x-6=0  x = 6

x+5=0  x = -5

x-9=0  x = 9

Therefore, x = 6, x = -5, x = 9 would be the correct answer.

Answer:

x = 8

Step-by-step explanation:

Angle bisector splits an angle into two equal angles

4x + 1 = 33

4x = 33 - 1

4x = 32

x = 32/4

x = 8

Answer:

x=8

Step-by-step explanation:

If AB is a bisector, that means  angles CAB and BAD are equal

<CAB = <BAD

33 = 4x+1

Subtract 1 from each side

33-1 = 4x+1-1

32 = 4x

Divide each side by 4

32/4 = 4x/4

8 =x

Answer:

Look at the picture.

Step-by-step explanation:

A height  of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the side opposite the vertex).

The answer to the question is A

Answer:

4

Step-by-step explanation:

16/4 = 4

if 75% of equipment is iron then do the math.

So it would be 4(2) + 4 = 75% of 16

So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods are [tex]\fbox{\begin \\\math{4}\\\end{minispace}}[/tex].

Further explanation:

Consider the number of woods as [tex]x[/tex] and number of irons as [tex]y[/tex].

Since the number of irons is four more than two times the number of woods, the number of irons is calculated as follows:

[tex]y=2x+4[/tex]                                                      ......(1)

The number of equipment consists of the woods and irons, therefore, the number of equipment [tex]n[/tex] is written as the sum of number of woods [tex]x[/tex] and number of irons [tex]y[/tex] as follows:

[tex]n=x+y[/tex]                                                                  ......(2)

From equation (1), substitute [tex]2x+4[/tex] for [tex]y[/tex] in above equation.

[tex]n=x+2x+4\\n=3x+4[/tex]

Since the total equipment contains [tex]75\%[/tex] of irons, it can be written as follows:

[tex]y=0.75n[/tex]

From equation(1) and (2) substitute [tex]2x+4[/tex] for [tex]y[/tex] and [tex]3x+4[/tex] for [tex]n[/tex] in above equation.

[tex]2x+4=0.75(3x+4)\\\Leftrightarrow2x+4=2.25x+\\\Leftrightarrow4-3=2.25x-2x\\\Leftrightarrow1=0.25x\\\Leftrightarrow x=1/0.25\\\Leftrightarrow x=4[/tex]

Substitute 4 for [tex]x[/tex] in equation (1) to obtain the number of irons.

[tex]y=2(4)+4\\y=8+4\\y=12[/tex]

Thus, the number of woods are 4 and number of irons are 12.

Learn more:  

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)  

https://brainly.com/question/1332667  

2. which is the graph of f(x) = (x – 1)(x + 4)?  

https://brainly.com/question/2334270  

Answer details:  

Grade: Middle school.  

Subjects: Mathematics.  

Chapter: Linear equation.  

Keywords: Linear equation, Function, Golf club, woods, y=2x+4, Variable, Middle term split method, Binomial, straight lines, Quadratic, Polynomial, Zeros, Zeros of a function, Expression, Equation, x, -x.

Answer:

Step-by-step explanation:

The question is to evaluate the natural logarithm of 5. Natural logarithms are logarithms with base e.

e is the irrational number equal to 2.71828182845904523536028747 ... (being irrational the decimals do not end and do not have a repetition period).

Logarithms are evaluated using tables or scientific calculators.

ln (5) = 1.6094379... it is also an irrational number, so it has infinite decimals with no repetition period.

So, rounding to two decimal numbers, ln (5) = 1.61, which is the option C).

Answer:c

Step-by-step explanation:test

Answer: D. 0.8125

Step-by-step explanation: His expenses is $975, and his salary is $1200. Divide the expenses by the salary to find the debt-to-income ratio.

975/1200 = 0.8125

The debt-to-income ratio is 0.8125.

Answer:

d) 0.8125

Step-by-step explanation:

Malcolm’s debt-to-income ratio is 0.8125 if his monthly expenses are $975 and his monthly salary is $1200.

All you have to do is divide monthly expenses by the monthly salary.

975 ÷ 1200 = 0.8125

Answer: y=-6/7x

Step-by-step explanation: A perpendicular slope is opposite reciprocal. The opposite reciprocal of 7/6 is -6/7. The equation of the perpendicular line is y=-6/7x.

first off, let's notice something, the graph seems a bit misleading, since the height of the nut is 0.5 cm, whilst the side of the base is 0.6 cm, however in the picture 0.5 appears longer.  That said

1)

the volume of the nut itself is simply the volume of a hexagonal prism, which will just be the product of the area of the hexagon and the height.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=0.5\\ p=\stackrel{0.6\times 6}{3.6} \end{cases}\implies A=\cfrac{(0.5)(3.6)}{2}\implies A=0.9 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the hexagonal prism}}{\stackrel{\textit{hexagon's area}}{(0.9)}~~\stackrel{\textit{height}}{(0.5)}\implies 0.45}[/tex]

2)

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=0.4\\ h=0.5 \end{cases}\implies V=\pi (0.4)^2(0.5)\implies V\approx 0.25[/tex]

3)

well, the composite figure is just a hexagonal nut with a cylindrical hole, so if we simply get the volume of the prism and subtract the volume of the cylindrical hole, what's leftover, is the volume of the nut alone without the hole.

[tex]\bf \stackrel{\textit{from 1)}}{0.45}~~-~~\stackrel{\textit{from 2)}}{0.25}\implies 0.20[/tex]

4)

in short, dividing the mass of 3.03 by our result from 3)

3.03 ÷ 0.2 = 1.515.

Answer:

The answer is 9

Step-by-step explanation:

When you divide 54 by 6 you get 9 because 10 times 6 equals 60 so if you minus 6 you get 54 which equals 6 times 9. :)

Answer:

9 or 9/1

Step-by-step explanation:

To convert improper fractions to whole numbers, you have to divide the numerator by the denominator.

So, 54 divided by 6 is 9

So 54/6 as a whole number 9

If you want to keep as a fraction it would be 9/1

Answer:

[-∞, 3)

Step-by-step explanation:

We are given the following inequality which we are to express as a set using the interval notation:

[tex] - 2 x + 3 0 > 4 x + 1 2 [/tex]

Rearranging the inequality by adding the like terms together to get:

[tex] - 2 x - 4 x < 1 2 - 3 0 [/tex]

[tex] - 6 x < - 1 8 [/tex]

[tex]x<\frac{-18}{-6}[/tex]

[tex]x<3[/tex]

Since the values of [tex]x[/tex] are lesser than [tex]3[/tex] so we can express this in interval notation as:

[-∞, 3)

Let the length = x and the width = y

For the length of fence we have x +x + y = 48 = 2x +y = 48

Rewrite as y = 48 - 2x

For the area we have x * y  = 254

Replace y in the are equation:

x * 48 -2x = 254

Simplify the left side:

48x - 2x^2 = 254

Subtract 254 from both sides:

48x - 2x^2 - 254 = 0

Using the quadratic formula solve for x:

a = -2, b = 48 and c = -254

x = -48 + 4√17/-4

x = 16.123 m.

The length = x = 16.123 meters.

The width = 48 - (16.123*2) = 15.754 meters

Rounding to the nearest centimeter:

Length = 16.1 ( 16 meters and 1 cm)

Width = 15.8 ( 15 meters and 8 cm)

Answer:

-6

Step-by-step explanation:

f(g(-1)) means we need to find g(-1) and then plug that result into f(x).

So let's start:

g(-1) means to replace the input variable in g(x)=x^2 with -1.

So we replace x with -1.  

g(-1)=(-1)^2

g(-1)=1

Now that we have g(-1) can be replaced with 1, we can further evaluate f(g(-1)).

So let's do that:

f(g(-1))

f(1)=1-7   ; I replaced the x in f(x)=x-7 with 1 to find f(1).

f(1)=-6

----

Putting altogether

f(g(-1))=f((-1)^2)=f(1)=1-7=-6.

Answer:

f(g(-1)) = -6

Step-by-step explanation:

* Lets explain how to solve the problem

- The problem is about the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted into

 another function.

- Ex: f(g(x)) is the composite function that is formed when g(x) is

 substituted for x in f(x)

* lets solve the problem

∵ f(x) = x - 7

∵ g(x) = x²

- We want to find f(g(-1))

* At first lets find g(-1) by substitute x in the function g(x) by -1

∵ g(x) = x²

∵ x = -1

∴ g(-1) = (-1)² = 1

* Now we want to find f(g(-1)), then we will substitute x in f(x) by

 the value of g(-1)

∵ g(-1) = 1

∵ f(x) = x - 7

∴ f(g(-1)) = f(1)

∵ f(1) = 1 - 7 = -6

∴ f(g(-1)) = -6

Answer:

four thousand one hundred

Step-by-step explanation:

expand the form

Answer:

193.8

Step-by-step explanation:

The 'mean' of a set is the set's average.

To find the average, add the terms together and divide by the number of terms.

[tex]108+305+252+113+191\\413+252+113+191\\665+113+191\\778+191\\969[/tex]

Divide by your number of terms (5).

[tex]\frac{969}{5} =193.8[/tex]

Answer:

193.8

Step-by-step explanation:

You add up all of the numers and get 969. Then you have to divide by the amount of numbers there are so divide by 5 and get 193.8

Step-by-step explanation:

i have answered ur question

The Perimeter of the given polygon can be calculated using the distance formula for each of its sides. The calculated distances are added to give a total perimeter of approximately 18.5 units.

The Perimeter of a polygon is calculated by adding the lengths of all its sides. Here, we need to calculate the distance between each pair of points, which gives the length of the sides of the polygon.

The distance between two points (x1, y1) and (x2, y2) is given by the formula sqrt((x2-x1)² + (y2-y1)²) .

To find the Perimeter of the polygon, we calculate the distances between each pair of vertices and then add them up:

Adding these distances, we get a perimeter of approximately 5 + 4.1 + 3.2 + 4.2 + 2 = 18.5 units, rounded to the nearest tenth of a unit.

https://brainly.com/question/15387363

#SPJ3

Answer:

I. 45.

Step-by-step explanation:

3 green peppers      g green peppers

--------------------     =  --------------------------

4 red peppers           60 red peppers

Using cross products

3 * 60 = 4 * g

180 = 4g

Divide each side by 4

180/4 =4g/4

45 = g

There are 45 green peppers

Answer:

Step-by-step explanation:

We know: measures of angles in a triangle add up to 180°.

Therefore we have the equation:

[tex]\gamma+\gamma+72^o=180^o[/tex]      subtract 72° from both sides

[tex]2\gamma=108^o[/tex]       divide both sides by 2

[tex]\gamma=54^o[/tex]

Answer:

[tex]\large\boxed{for\ (-3,\ 2):\ y-2=-\dfrac{1}{5}(x+3)}\\\boxed{for\ (2,\ 1):\ y-1=-\dfrac{1}{5}(x-2)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

========================================

We have the points (-3, 2) and (2, 1).

Substitute:

[tex]m=\dfrac{1-2}{2-(-3)}=\dfrac{-1}{5}=-\dfrac{1}{5}[/tex]

for (-3, 2)

[tex]y-2=-\dfrac{1}{5}(x-(-3))\\\\y-2=-\dfrac{1}{5}(x+3)[/tex]

for (2, 1)

[tex]y-1=-\dfrac{1}{5}(x-2)[/tex]

Answer:

C

Step-by-step explanation:

When we set the numerator equal to 0 and solve for x, that value is the horizontal asymptote (a line the graph come towards, but never crosses).

Looking at the graph, the horizontal asymptote is x = 2, so which one of the 4 functions has a horizontal asymptote of 2? Let's check.

A) 2x - 1 = 0

x = 1/2

B) same, x = 1/2

C) 2x -4 = 0

x = 2

D) same as A,B, x = 1/2

As we can see, option C has the right horizontal asymptote and A,B,D are eliminated. So answer is C.

Answer:

Divide and express 2.7/1.1 to the nearest tenth.

Step-by-step explanation:

Answer:

[tex]x \geq\frac{2}{3}[/tex]

Step-by-step explanation:

The question is  [tex]3x+5 \geq 7[/tex]

We simply take the numbers to one side and variables to one side and solve via algebra (shown below):

[tex]3x+5 \geq 7\\3x \geq 7-5\\3x \geq 2\\x \geq\frac{2}{3}[/tex]

This range of values is the solutions of the inequality.

Answer:

A

Step-by-step explanation:

3x-5≥19

Add 5 to each side

3x-5+5≥19+5

3x ≥ 24

Divide each side by 3

3x/3 ≥24/3

x ≥8

Since this is greater than or equal to there is a closed circle at 8

greater than means the line goes to the right

Answer:

2.45 or 2 9/20

Step-by-step explanation